Explores curvature, inflection points, and angular functions in plane curves, highlighting the importance of inflection points.
Introduces hyperbolic geometry, covering complete metric spaces, isometries, and Gaussian curvature in dimension 2.
Explores curves in the oriented plane, discussing orientation, vector spaces, equivalence relations, and curvature of regular curves.
Covers symmetry in modern geometry, reflections, translations, rotations, compositions of isometries, fundamental theorems, configurations of lines and planes, and surface analysis.
Explores the derivative of curve lengths, fixed-end deformations, geodesics, surface point typologies, and sphere parametrization.
Discusses curved space-time, arguments against scalar gravity, and relativistic effects of motion.
